The present invention relates to a system and a method for measuring the alternating current equivalent series resistance of a conductor, in particular when transporting a large current, i.e. of the order of a few thousand Amperes (around 3000 A).
When carrying an alternating electric current, at a frequency of 50 Hz for example, a conductor will exhibit an impedance having a real or active component and an imaginary or reactive component. Measurement of the alternating-current resistance refers to the value, per unit length (xcexa9/m), of the real component of the impedance of the conductor.
Today, as a result of the rapid increase in the power required by electrical systems, cables are made for high voltage with conductors of greater than 1000 mm2 cross-section. In order to be able to assess the performance of a cable of this kind and quantify the magnitude of the power losses it is important to know the value of the alternating current equivalent, series resistance of a conductor.
With conductors of such dimensions the nonuniform distribution of current within the cross-section causes a considerable rise in the alternating current equivalent series resistance. As is known, this phenomenon is due principally to two effects referred to as the skin effect and the proximity effect.
The skin effect corresponds to the tendency of the alternating current to flow close to the surface of a conductor, thereby reducing the useful cross-section for passage of the current and increasing the resistance thereof.
The proximity effect entails a redistribution of the current in the conductor, due to the closeness of another conductor.
Considering the difficulty of applying traditional methods of calculating resistance, such as those discussed in the articles listed below and from the CEI (Commission Electronique International) 287 standard, to the conductors used in practice, made up of a very large number of wires more or less insulated from one another, the only means of assessing the alternating current equivalent series resistance is through experimental methods.
The articles relating to the methods of calculation are: xe2x80x9cEddy current losses in single-conductor paper insulated lead covered unarmoured cables of single-phase systemxe2x80x9d, A. H. Arnold, Vol. 89, Part II, J. IEE, p. 636, 1942; and xe2x80x9cProximity effect in solid and hollow round conductorsxe2x80x9d, A. H. Arnold, Vol. 88, Part. II, J. IEE, p. 349-359, 1941.
Measurement of the alternating-current resistance is of considerable interest both in the course of research, where it is used to improve the design of the conductor, and in industry, for testing the finished product.
In particular, the method used must guarantee the typical repeatability and accuracy of the methods employed in the course of research, but must be sufficiently simple to be industrially applicable.
Measurement of the alternating-current resistance must take into account the temperature of the cable, the frequency of the flowing current, and the closeness of other conductors.
The alternating-current resistance of cables of 1000 mm2 cross-section is of the order of 10xe2x88x924xe2x88x9210xe2x88x925 xcexa9/m and the accuracy of the measurement should be at least 0.1%.
One technique for measuring the alternating-current resistance makes use of networks of the bridge type on account of their simplicity and the absence of initial calibrations.
A bridge network consists of a quadrilateral of impedances, one of which is unknown. A null indicator (normally consisting of a galvanometer) is inserted into one of the diagonals, and the power supply into the other. By modifying the value of one or more arms, of known value, so as to zero the null indicator, the value of the unknown impedance is derived from the value of the other impedances. The accuracy of a bridge system depends directly on the accuracy of the known impedances.
For example, an accuracy of measurement of around 0.2% is achievable with impedances having an accuracy of 0.1%. Better accuracies can be obtained only with special preliminary calibrations.
Furthermore, if harmonic contributions at frequencies higher than the working frequency are present in the current flowing in the conductor, as normally happens, measurement with the bridge could overestimate the value of the resistance. The article by F. Castelli, L. Maciotta-Rolandin, P. Riner entitled xe2x80x9cA new method for measuring the AC resistance of large cable conductorsxe2x80x9d, published in March-April 1977 in IEEE Transactions on Power Apparatus and Systems, vol. PAS-96, No. 2 pp. 414-422, describes a bridge for measuring alternating-current resistance, based on the so-called Maxwell bridge which uses a transformer in one arm in such a way that the measurement bridge is not traversed by the high current of the conductor.
The measurement of the alternating-current resistance can be derived from the ratio between the real component of the voltage withdrawn over a predetermined length of the conductor and the current flowing in this conductor. With the current flowing in the conductor known, the measurement of the voltage can be effected with an instrument capable of discriminating and measuring the real component from the imaginary one. An instrument of this type is the so-called lock-in amplifier, such as for example that sold by Stanford Research Systems, 1290-D Reamwood Ave., Sunnyvale, Calif., model SR-830.
This amplifier has a measurement accuracy (or gain accuracy) equal to 1%, deemed insufficient for measuring alternating-current resistance.
German patent DE-1,067,924 discloses a network test device for determining the short circuit current intensity in a network of electrical conductors. In that device a load resistor is syncronously connected and disconnected with a frequency depending on the network frequency. The load resistor temporarily lowers the network voltage. An indicator shows the voltage difference between the connected and the disconnected status. The voltage of the periodically loaded network is sent to two channels. A first channel comprises a variable delay line, a second channel comprises a variable attenuator. The average of the sum (or difference) voltage between the two channels is measured by a rectifier instrument. The two channels are then equalized so that the instrument gives a zero reading in case of unloaded network. The frequency of connection and disconnection of the load resistor can be different from the network frequency, e.g., one half or one third or even double the network frequency.
German patent DE-1,073,621 disclose a method for measuring the internal network resistance (impedance and phase angle) at the network frequency. The method employs a measuring voltage at a frequency higher (harmonic) than the network frequency and a dummy load that is switched to the network terminals with the network frequency. The load current is flown in a compensation device comprising a variometer with a switchable conversion ratio and an ohmic resistance, from which a sum voltage is derived. The sum voltage has a component in phase with the load current and a component advancing in phase by 900 the load current and is adjustable in intensity by the variometer. The sum voltage is switched against a voltage derived from the network voltage. The signal resulting from two voltages is bandpass filtered at the frequency of the measuring voltage and read in an instrument. The variometer and a potentiometer are adjusted until a null reading is achieved on the instrument. The phase angle measurement is then carried out by reading the variometer setting. The instrument is then switched to measure the sum voltage, while at the same time the variometer conversion ratio is switched to a second value. A measurement of the internal impedance of the network is so derived.
The Applicant has found that the measurement accuracy can be greatly increased, beyond the accuracy limit of the available instrument, by measuring with the latter not the value of the quantity to be measured, but rather the difference between the said quantity and a known and adjustable quantity. In this way the measurement error of the instrument, proportional to the value of the actual measurement, can be reduced by making the said difference tend to zero, or in any event by taking the said difference to a value such that the relative error of measurement is less than a predefined value.
In a first aspect the present invention relates to a method for measuring the series resistance of a conductor traversed by an alternating current comprising the phases of:
measuring at least a real component of a voltage drop over a predetermined length of the said conductor;
deriving a measurement current from the said conductor, the said measurement current having a real component only and having a predetermined relationship with the said alternating current; characterized by
converting the said measurement current into a corresponding measurement voltage having a predefined conversion ratio with the said measurement current;
withdrawing an adjustable portion of voltage from the said measurement voltage;
comparing the said adjustable portion of voltage with the said voltage drop;
adjusting the said adjustable portion of voltage in such a way as to balance the said voltage drop;
measuring the said adjustable portion of voltage which balances the said voltage drop;
measuring the said alternating current; determining the resistance as a function of the value of the said adjustable portion of voltage which balances the said voltage drop and of the value of the said alternating current.
For the purposes of the present invention, in order to balance the voltage drop it is intended to generate a corresponding voltage of a value such that the difference between the said generated voltage and the said voltage drop is substantially close to zero (to within a value correlated with the desired degree of accuracy of measurement).
Preferably, the phase of measuring the said alternating current comprises the phases of:
measuring the said measurement voltage;
determining the value of the said alternating current as a function of the said measured measurement voltage, of the said predefined conversion ratio and of the said predetermined relationship.
Preferably, it further comprises the phase of eliminating the imaginary component of the said voltage drop.
In particular, the phase of eliminating the imaginary component of the said voltage drop comprises the phases of:
measuring an imaginary component of the said voltage drop;
withdrawing a further adjustable voltage from the said conductor, having an imaginary component only;
comparing the said further voltage with the imaginary component of the said voltage drop;
adjusting the said further voltage in such a way as to balance the said imaginary component of the said voltage drop.
Preferably, the phase of deriving a measurement current from the said conductor comprises associating a measurement transformer with the said conductor, able to generate the said measurement current in correlation with the said alternating current.
Preferably, the said predetermined relationship is dependent on the transformation ratio of the said transformer.
In a preferred form the phase of converting the said measurement current comprises passing the said measurement current through a resistor of predefined value.
In particular the said predetermined relationship is dependent on the predefined value of the said resistor.
In particular the said phase of withdrawing an adjustable portion of voltage comprises connecting a voltage divider in parallel with the said resistor.
In particular the said phase of comparing comprises supplying the said voltage drop and the said adjustable portion of voltage to a null indicator.
In a further aspect the present invention relates to a method for measuring the series resistance of a conductor traversed by an alternating current comprising the phases of:
measuring at least a real component of a voltage drop over a predetermined length of the said conductor;
deriving a measurement current from the said conductor, the said measurement current have a real component only and having a predetermined relationship with the said alternating current; characterized by
converting the said measurement current into a corresponding measurement voltage having a predefined conversion ratio with the said measurement current;
withdrawing a portion of voltage from the said measurement voltage;
comparing the said portion of voltage with the said voltage drop;
measuring the difference between the said portion of voltage and the said voltage drop;
selecting the said portion of voltage at a known value such that the said difference is less than a predefined value;
measuring the said alternating current;
determining the resistance as a function of the value of the said known value of the said portion of voltage, of the said difference and of the value of the said alternating current.
In a further aspect the present invention relates to a system for measuring the series resistance of a conductor traversed by an alternating current comprising:
a voltage sensor applied over a predetermined length of the said conductor able to deliver a measured voltage having at least a real component;
a current sensor applied to the said conductor able to deliver a measurement current having a real component only, and having a predetermined relationship with the said alternating current;
a current/voltage converter having a predefined conversion ratio with the said measurement current, for converting the said measurement current into a corresponding voltage;
a voltage divider capable of delivering an adjustable division of the said corresponding voltage;
a null indicator receiving the said measured voltage and the said adjustable division, able to indicate the balancing between the real components of the said measured voltage and of the said adjustable division;
a voltage meter able to deliver the value of the said adjustable division and the value of the said corresponding voltage;
means of calculation able to determine the value of the resistance as a function of the value of the said adjustable division, of the value of the said corresponding voltage, of the said predetermined relationship and of the said predefined conversion ratio.
Preferably it further comprises a variable mutual inductance associated with the said conductor and able to deliver a variable voltage having an imaginary component only and a null indicator able to indicate the balancing between the imaginary component of the said measured voltage and the said variable voltage delivered by the said variable mutual inductance.
Preferably the said null indicator consists of a vector voltmeter.
More preferably the said null indicator consists of a lock-in amplifier.
In particular the said voltage meter is a meter having an accuracy of greater than 0.1%.
Preferably the said current/voltage converter comprises a resistor through which the said measurement current flows; said resistor has an inductance value of less than 1 xcexcH.
In particular the said voltage divider comprises a variable potentiometer connected in parallel with the said resistor; the said potentiometer has an inductance value of less than 1 xcexcH.
In particular the said resistor has an accuracy of greater than 0.1%.
Preferably the said current sensor comprises a transformer operatively connected to the said conductor.